Names are a very important thing among the Clans, and they change as a marker to each stage in a cat's life. As a kit, all names will be followed by kit so that when speaking of that cat, other cats know what stage in his or her life it has passed. For example. If a cat were called thunderkit when it is born, when it turns six moons and becomes an Apprentice, it will be called thunderpaw. When the apprentice is deemed worthy, a naming ceremony will be held and he or she will recieve their warrior name.
This name varies from cat to cat and it is up to the leader to name the cat when he or she becomes a warrior. In this case, we will give thunderpaw the name Thunderpelt, but it could easily have been Thundertooth, Thunderheart, Thunderfoot, Thunderstripe, etc. Names are ususally given based on a trait that that cat carried. For example, if a cat has a broken tail, he could be called Brokenpaw during his apprenticeship but he would be called Brokentail when he recieves his warrior name.
Leaders have another stage that most cats do not receive. When they go to Moonstone and receive their nine lives, they take the name star. She if we go back to Thunderpelt from the before example, he is a warrior and he makes the trip to Moonstone. He would then become Thunderstar.
When you join, join only with the first part of your name. StarClan (me) will then give you your name depending on your age and occupation.